Weighted integral Hankel operators with continuous spectrum

TY - JOUR

T1 - Weighted integral Hankel operators with continuous spectrum

AU - Fedele, Emilio

AU - Pushnitski, Alexander

PY - 2017/10

Y1 - 2017/10

N2 - Using the Kato-Rosenblum theorem, we describe the absolutely continuous spectrum of a class of weighted integral Hankel operators in $L^2(\bbR_+)$. These self-adjoint operators generalise the explicitly diagonalisable operator with the integral kernel $s^\alpha t^\alpha(s+t)^{-1-2\alpha}$, where $\alpha>-1/2$.Our analysis can be considered as an extension of J.~Howland's 1992 paper which dealt with the unweighted case, corresponding to $\alpha=0$.

AB - Using the Kato-Rosenblum theorem, we describe the absolutely continuous spectrum of a class of weighted integral Hankel operators in $L^2(\bbR_+)$. These self-adjoint operators generalise the explicitly diagonalisable operator with the integral kernel $s^\alpha t^\alpha(s+t)^{-1-2\alpha}$, where $\alpha>-1/2$.Our analysis can be considered as an extension of J.~Howland's 1992 paper which dealt with the unweighted case, corresponding to $\alpha=0$.

KW - Weighted Hankel operators

KW - Absolutely continuous spectrum

UR - https://www.scopus.com/pages/publications/85094078019

U2 - 10.1515/conop-2017-0009

DO - 10.1515/conop-2017-0009

M3 - Article

SN - 2299-3282

VL - 4

SP - 121

EP - 129

JO - Concrete Operators

JF - Concrete Operators

IS - 1

ER -